Patrick Dorgu scored a stoppage-time equaliser after Joshua Zirkzee had reduced the deficit, rescuing a point for Michael Carrick's side after Aston Villa appeared to be heading towards a comfortable victory.
Aston Villa made a sensational start to the encounter, taking the lead after just one minute through Alysson, who finished brilliantly after a move involving John McGinn and Nicolas Jackson.
The visitors doubled their advantage only three minutes later when Jackson capitalised on a rebound following Alysson's effort to make it 2-0.
Manchester United responded and were awarded a penalty in the 16th minute after Matheus Cunha was brought down inside the box. Captain Bruno Fernandes stepped up and calmly converted to reduce the deficit.
The hosts continued pushing forward and eventually found their equaliser just before half-time. Noussair Mazraoui pulled the ball back for Youri Tielemans, whose finish in the 44th minute brought United level at 2-2.
However, Aston Villa regained control shortly after the restart. John McGinn converted a penalty in the 48th minute to restore the visitors' lead.
Villa extended their advantage in the 53rd minute when Leon Goretzka found the back of the net, putting Unai Emery's men 4-2 ahead.
With Manchester United struggling to find a response, the visitors appeared to have secured all three points.
However, the hosts refused to give up and mounted a remarkable late fightback.
Joshua Zirkzee pulled one back in the 90+2nd minute, giving United renewed hope of salvaging something from the encounter.
The drama reached its climax in the 90+6th minute when Patrick Dorgu rose to head home from a corner, completing an incredible comeback and sending Old Trafford into celebration.
Aston Villa were left frustrated after surrendering a two-goal advantage in the closing stages, while Manchester United celebrated a valuable point.
Despite the dramatic comeback, United remain in the Premier League relegation zone, sitting 18th with eight points from 10 matches.
Full-time: Manchester United 4-4 Aston Villa
Goalscorers:
• Manchester United: Bruno Fernandes 16' (pen), Youri Tielemans 44', Joshua Zirkzee 90+2', Patrick Dorgu 90+6'.
• Aston Villa: Alysson 1', Nicolas Jackson 4', John McGinn 48' (pen), Leon Goretzka 53'.
Competition: English Premier League, Matchday 10.
Venue: Old Trafford, Manchester.